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Random Numbers Zachary Neyland

Random Numbers Zachary Neyland. Definitions. Random number – a random number is a number that is generated by a process whose outcome is unpredictable and typically cannot be reproduced Seed – starts the process for generating random numbers

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Random Numbers Zachary Neyland

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  1. Random NumbersZachary Neyland

  2. Definitions • Random number – a random number is a number that is generated by a process whose outcome is unpredictable and typically cannot be reproduced • Seed – starts the process for generating random numbers • Period – the length a given series of random numbers has before repeating a number

  3. Types of Random Number Generators • Pseudo-Random Number Generators • Not truly random • True Random Number Generators • Extract randomness from physical phenomena

  4. Pseudo-Random Number Generators • Linear congruential method • An example simple linear formula • Xn+1 <- (k*Xn + C) mod M • Sample sequence (k = 19, C = 51, M = 100, X0 = 25): • 25, 26, 45, 6, 47, 44, 87, 4, 27, 64, 67, 24, 7, 84, 47

  5. True Random Number Generators • Need to use physical phenomena • Zener diode • Radioactive decay • Atmospheric noise/radio noise • Sample and convert to a 1 or 0

  6. PRNGs vs TRNGs

  7. OH GOD MY BRAIN • Impossible to verify that a given number was produced randomly • Very easy to determine if a sequence of infinite length is random • Random if quantity of information it contains is also infinite

  8. Applications of Random Numbers • Cryptology/Security • Game and gambling • Random Sampling (drug screening, exam questions) • Lotteries

  9. References • http://www.random.org • A.K. Dewdney The (new) Turing omnibus, New York Henry Holt and Company

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